- © 2015 by the Seismological Society of America
Online Material: Tables of questions and answers of the macroseismic questionnaire, score matrices, and a figure showing a macroseismic field example.
Macroseismic investigation with data collected through web‐based questionnaires is today routinely applied by most important seismological institutions, such as the U.S. Geological Survey (http://earthquake.usgs.gov/earthquakes/dyfi/; last accessed December 2014), British Geological Survey (http://www.earthquakes.bgs.ac.uk/questionnaire/EqQuestIntro.html; last accessed December 2014), European‐Mediterranean Seismological Centre (http://www.emsc-csem.org/Earthquake/Contribute/choose_earthquake.php?lang=en; last accessed December 2014), Schweizerische Erdbebendienst (http://www.seismo.ethz.ch/eq/detected/eq_form/index_EN; last accessed December 2014), Bureau Central Sismologique Français (http://www.seisme.prd.fr/english.php; last accessed December 2014), and the New Zealand GeoNet project (http://www.geonet.org.nz/quakes/; last accessed December 2014). The wide diffusion of Internet and the citizen collaboration (crowdsourcing) allow documentation of information on seismic effects and production of a macroseismic field with low costs and almost in real time. Transformation from qualitative information (as given by questionnaires) to numerical quantification is a crucial issue. In the traditional evaluation of intensity, experts used to work through a complex comparison of effects basically driven by personal experience. The major problem with this approach concerns the difficulty in verifing and reproducing the evaluation process due to the lack of a detailed explanation of the employed workflow and to the large variability of possible cases. On the other hand, an automatic method for the estimation of macroseismic intensities needs to be completely well defined and specified in order to be reproducible and verifiable. For these reasons, this paper presents a comprehensive explanation of our intensity assessment method.
A useful automatic method for intensity assessment should be computationally fast and strictly follow the macroseismic scales. To meet these requirements in 2010, we proposed a method that firstly quantified the effects using additive scores associated with each answer of the questionnaire item and then determined an intensity estimate for each questionnaire (Sbarra et al., 2010). After a trial period and having collected more than 500,000 questionnaires, we were able to thoroughly test the method. As a result of this testing, we describe here a new improved method that takes into account further factors, such as the situation and the location of the observer (Sbarra et al., 2012, 2014), to obtain a more accurate estimate of the macroseismic intensity degree at the municipality level.
In this paper, we show some applications of our method with reference to the Mercalli–Cancani–Sieberg (MCS) scale, because this scale has long been used with Italian earthquakes and allows easy comparison between these intensities and other traditional ones.
QUESTIONNAIRE AND SCORE MATRICES
The Istituto Nazionale di Geofisica e Vulcanologia (INGV) collects online macroseismic questionnaires (http://www.haisentitoilterremoto.it; last accessed December 2014, in Italian) about events felt in Italy, voluntarily filled in by citizens. Some of these people (more than 23,000) are registered users who are alerted via email after the occurrence of an earthquake near their municipalities.
The questionnaire has been online since 2007 and asks participants to describe personally observed effects (Sbarra et al., 2010). The questionnaire (see Table S1, available in the electronic supplement to this article) consists of simple questions with multiple answers defined following both the MCS scale and the European Macroseismic Scale (EMS). The questions concern many effects, ranging from transient ones to building damage. The analysis of the questionnaire data for the evaluation of the local macroseismic intensity is performed by a dedicated automatic procedure to produce intensity maps that are published in real time on the website and updated as soon as new data are available.
We do not differentiate macroseismic intensities lower than II, and, in fact, we consider degree I as indistinguishable from II in the web questionnaire because people recognizing the earthquake occurrence, following the degree II definition, are so few (about 5%) that they are unlikely to submit questionnaires. Thus, we consider the not‐felt area as characterized by degrees I and II. Likewise, we group the higher degrees (>VII) into a single class, because they need direct evaluations by experts for a correct assessment; the same criterion is followed by the European‐Mediterranean Seismological Centre (Musson, 2007).
The correspondence between answers and degrees is obtained through a score matrix specifically created for each intensity scale (see Tables S2 and S3 for the MCS scale and EMS, respectively). In the matrix, each row represents an answer and the columns refer to the associated macroseismic intensities. A score equal to 1 is given when the considered answer points to a specific intensity, otherwise the score is 0. The score matrix represents the formalization of answers to properly quantify each effect for intensity assessment. Macroseismic scales use words such as “few,” “many,” and “most” to categorize the percentage of occurrence of effects. Such amounts were converted into percentage ranges for each macroseismic scale (Grünthal, 1998; Molin et al., 2008). When creating the score matrix, we assumed the compiler and the observed building belong to the “many” category, which is the wider category and thus the most probable one. Some answers point to a specific intensity degree and assign 1 to the score of that degree, whereas other answers are less specific and are associated with a range of intensity degrees to which they assign 1. The answers explicitly excluding an effect add scores to degrees lower than the degree specific of the effect itself; for example, a small object that is still (not in motion) at higher floors assigns 1 to degrees III and IV, because small objects move at degree V. Degree I–II is assigned only in the case of not‐felt earthquakes. In the questionnaire, there is always the answer ‘‘unable to say,’’ which must be considered as an option different from the absence of the effect and does not assign any scores.
The score matrices take into account all the possible situations and localizations of the observer as well as the building materials, to consider all the combinations of the conditions described in the seismic scales. For example, the perceived intensity of shaking changes if the compiler is at rest or in motion or is at a higher floor rather than outdoors; moreover, damage must be considered differently depending on building materials and typology. To this regard, the considered variables are “Situation” of the compiler during the earthquake event (sleeping, at rest, in motion), the “Location” where the respondent is (indoor at underground or ground level, indoor at floors from first to tenth, outdoors), and the “Building” material of the structure in which the observer was at the time of the event (masonry, reinforced concrete, and, only for EMS, wood, steel). The variable Situation has an influence only on the scores of the question about the felt vibration; Location modifies the scores of all the transitory effects; and, Building influences the scores of damage. Concerning Location on the basis of the experimental results obtained from the database www.haisentitoilterremoto.it used in Sbarra et al. (2010), we consider together the answers “underground” and “ground level,” as well as all the levels from the first floor to the tenth, whereas floors higher than tenth are presently discharged as rarely present in Italy and with a poorly studied behavior. According to the description of macroseismic scales, location should have more weight than situation. On the contrary, Sbarra et al. (2014) indicated the situation had the same or more influence on earthquake perception. In particular, people, even if located on the same floor, perceive a stronger vibration if at rest rather than in motion, with a difference of about 0.5 intensity degree; on the other hand, there is a difference smaller than 0.5 for observations made outdoors and at lower floors while at rest (Sbarra et al., 2014).
INDIVIDUAL INTENSITY COMPUTATION
For each questionnaire, the intensity distribution is computed by summing, for each intensity degree, the scores of all answered items associated with that degree. The mode of this distribution constitutes the intensity degree most often identified by the effects reported by the observers. Sometimes the intensity distribution does not show a unique mode, as some local maxima may occur. We define a local maximum as the intensity corresponding to a score value greater than 95% of the modal score value. In this case, the individual intensity is computed as the weighted average of the local maxima. In the case of a not‐felt response, we just assign degree I–II.
Questionnaires may contain incorrect answers or insufficient information; these factors usually modify the score distribution by increasing the variance or decreasing the score value of the mode. Overall, the rejection of a bad‐quality questionnaire is made using the following criteria.
Intensity discrepancy: Rejection occurs if the computed intensity is less than 3 units or more than 2.5 units away from the intensity (Int) obtained using the intensity prediction equation (IPE) (1)which is estimated on a selected subset of data (R is the hypocentral distance in km, and ML denotes the local magnitude).
Contradictory answers: Rejection occurs if there are more than three local maxima, the local maxima are separated by more than one degree, or the mean value of local maxima divided by the mean of the other values (a sort of signal‐to‐noise ratio) is smaller than a threshold, experimentally set to 1.4.
Scarcity of information: Rejection occurs if any degree receives less than three answers.
Duplicate entries: Rejection occurs if the questionnaire was sent more than once by mistake, thus is identical to a previous one received shortly before.
The percentages of rejected questionnaires are quite low: 0.9% due to intensity discrepancy and 2.6% for both contradictory answers and scarcity of information.
MUNICIPALITY INTENSITY ASSESSMENT
With the term “municipality,” we mean the territory that is inside one of the 8092 administrative boundaries into which Italy is subdivided. A municipality can enclose more than one small town, and the average size is 37 km2. The answers of all questionnaires from a municipality are taken into account for computing its macroseismic intensity. In particular, the score distribution of each questionnaire is normalized such that the highest score value (the one corresponding to the modal intensity) is set to 1; then all the individual scores are summed up and a new intensity distribution is obtained at the municipality level. Using this distribution, the municipality intensity is computed as the average of local maxima (as before, they are defined as the values greater than 95% of the modal score) weighted with the relative frequencies. In Figure 1, examples of the MCS score distribution for three municipalities are shown. In particular, Figure 1a refers to Poggio Renatico for the ML 5.9 Emilia earthquake of 20 May 2012. The score distribution is wide (including scores from III to >VII) with mode VI and a local maxima VII; the computed weighted average is 6.49, thus the assigned intensity is MCS VI–VII.
Another important issue for a correct evaluation of the municipality intensity involves the estimation of the percentage of not‐felt reports. As established by intensity scales, low‐intensity degrees are assessed by taking into account both the effects and the percentage of people who felt the shaking. As generally occurs using online surveys, not‐felt reports are undersampled (Boatwright and Phillips, 2012). This is basically due to the propensity of people to complete the questionnaire only in cases of felt earthquakes. To increase the not‐felt participation, in 2009 we began inviting people to become registered users to inform them of all the events that occurred near their municipality. In this way, they are invited to reply through the questionnaire even when they did not feel the quake. Despite the presence of registered observers, the not‐felt reports remain undersampled. This behavior is conditioned by many factors, among them magnitude, felt intensity, media consideration, Internet diffusion, and geographic area. We thus analyzed the responses of a sample of municipalities in the case of an earthquake felt by all (MCS≥VI) and of another one not felt (MCS I–II); in the first case, the responses were on average ten times greater than in the second case, so the mean underestimation extent was quantified as a factor of 10. By using this factor, we obtained the corrected felt percentages comparable with the quantifications given by Molin et al. (2008) for the MCS scale and Grünthal (1998) for EMS. If the degree pointed out by the corrected felt percentage is less than the modal score value, then the final macroseismic intensity assigned to a municipality is calculated by averaging the first intensity with the second one, respectively, weighted with the number of not‐felt and felt responses. Figure 1b refers to Perugia for the ML 4.2 Tevere Valley earthquake of 15 December 2009; it shows the case in which the corrected felt percentage is 65%, corresponding to MCS V, a value greater than the modal value (IV). We think that, in this case, the correction factor was not sufficient to reach the felt percentage relative to the modal value, which is based on a greater amount of information, thus we assess the intensity considering only the modal value. Figure 1c shows the score distribution of Rome for the ML 3.6 earthquake that occurred in central Italy on 13 July 2011; in this case, by applying the aforementioned correction factor of not‐felt responses, we obtain a felt percentage of 4%, corresponding to degree II. The average among the modal value (III), weighted by the number of the felt questionnaires (115), and the degree obtained with the felt percentage (II), weighted by the number of not‐felt questionnaires (302), is 2.28, confirming the MCS II assigned to the city.
We consider the macroseismic intensity of a municipality sufficiently reliable if it is calculated using at least five responses (the same criterion is followed by Mazet‐Roux et al., 2010). The intensities calculated with less than five responses are shown on the online map using a very small dot (see Fig. S1) to compare them with other spatially close intensities.
COMPARISONS WITH TRADITIONAL METHOD
In this section, we compare the MCS intensities estimated using our automatic method with all the available ones obtained using onsite surveys by an INGV team of experts (Quick Earthquake Survey Team [QUEST] Working Group, http://quest.ingv.it/; last accessed December 2014, in Italian; Camassi et al., 2008; D’Amico et al., 2009; Galli et al., 2009; Arcoraci et al., 2012, 2013). In this regard, the bubble plot in Figure 2 represents the intensities of 106 municipalities pertaining to five earthquakes, the strongest one (ML 5.8) occurred on 6 April 2009 in central Italy. The intensities reported on the x axis (QUEST–MCS) are assessed by the expert team, whereas the ones on the y axis (web‐MCS) are obtained through our web‐based method for the same municipalities and earthquakes (note that intermediate half‐degree intensities represent uncertain attributions that occur in cases of bimodal intensity distribution). The straight and dotted lines in the plot represent the bisector (y=x) and the functions y=x±1, respectively. In particular, the region defined by the dotted lines represents the range of intensities ΔInt=±1. All but three municipality intensities fall inside this range, meaning that the two methods provide similar results. In particular, most of the cases (99 of 106) are located on or under the bisector, making it possible to conclude that the results are in agreement, though with a slight underestimation made by our web evaluation. It is worth noting that the comparison with the traditionally assessed values is not always straightforward; this happens because the INGV team of experts sometimes assigns an intensity to suburbs or to the historical center of towns instead of to the entire municipality. Such historical centers have older buildings that are more vulnerable to the shaking action of earthquakes. For example, with the ML 5.8 central Italy event, the QUEST report specifies that historical centers showed an intensity 3 degrees higher with respect to other zones of the towns.
Our database counts more than 23,000 municipality MCS‐intensity data points, each computed using at least five questionnaires. To express intensity as a function of magnitude and distance, we simplified the analysis assuming intensity as a continuous variable and plotting the MCS averages calculated inside windows 0.02logR wide for each 0.1 magnitude step (Fig. 3). A few high‐intensity values are located in the upper left portion Figure 3, whereas most of data refer to low intensities. A least‐squares regression surface of averaged intensities, excluding the flat degree‐II region (shaded squares), was obtained: (2)It is drawn with contour lines in Figure 3 and well represents the overall behavior of the data, even if it fails to reproduce the steep increase of intensity approaching the epicenter of the strongest earthquakes. The proposed regression mainly applies to MCS III and IV, which are the cases most represented by our data. This form of IPE, like the generic Int=a+bM+clogR with c=0, gathered from studies on peak ground acceleration (Musson, 2005), is particularly simple and can be used to calculate the mean felt area.
In Figure 4, an overview of several IPEs, drawn on the same plot using colored contour lines, is given. The values expressed in different macroseismic scales—MCS, EMS, and modified Mercalli intensity (MMI)—can be compared considering their similarity (Musson et al., 2010). The relations come from different assessment methods, different datasets (traditional, web questionnaires), and different geographic regions (Italy, United Kingdom, U.S.A.), but for low magnitudes and long distances, the values given are quite similar. For low intensities (Int≤VI), equation (2) is in good agreement with the relation for California by Atkinson and Wald (2007), computed (like our relation) with data from online responses, whereas for higher intensities it reaches a difference of 1°, probably due to the scarcity of intensities Int>V in our database.
CONSIDERATIONS AND CONCLUSIONS
According to Musson and Cecić (2012), the automatic intensity evaluation can be made following either regression‐based and expert‐like approaches. The first produces results in agreement with past datasets through a regression between automatic scores and human‐assigned traditional intensities. We instead adopt the expert‐like approach that closely follows the indications of a macroseismic scale. However, we constantly use our experimental data to test the intrinsic coherence of the macroseismic scale in search of possible improvements. For example, in Sbarra et al. (2012, 2014) we assess the great influence of situation and location on the perception of shaking intensity.
The score distributions at the municipality level (e.g., Fig. 1) usually cover a wide range of intensities. This result mirrors reality in villages where macroseismic intensity is the result of the sum of many different effects. For this reason, the use of an automatic algorithm is useful for achieving an unbiased intensity assessment. The evaluation of the results over time suggests the mode of the distribution gives a better estimate with respect to the average of individual intensity used in the previous version of our method (Sbarra et al., 2010). In fact, the average‐based method had a tendency to favor central values. The comparison of the results estimated with our automatic method with the ones traditionally assigned through onsite survey showed a general agreement in the variability range of ±1 intensity (Fig. 2), with a tendency of our estimates to be lower than the traditional values.
The proposed method has a modular structure created to include different macroseismic scales just by adding new score matrices and to allow future refinements. In fact, we believe that macroseismic scales are not static, but they instead should be updated on the basis of new experimental observations, as in the case of a recent study (Sbarra et al., 2015) that suggests the existence of nontrivial building height effects on felt intensity. This result could influence the construction of score matrices. Moreover, in our questionnaire there are some questions about effects (e.g., earthquake sound, earthquake lights) which are not currently used for intensity assessment but could be useful for further evaluations (Tosi et al., 2012).
We thank M. Cameletti for careful reading and helpful advices. We are grateful to C. Cauzzi and to an anonymous reviewer for their accurate suggestions. We acknowledge D. Sorrentino for information technology architecture of http://www.haisentitoilterremoto.it (last accessed December 2014; in Italian).